If `A=[(1,2),(0,1)], then A^n=`
(A) `[(1,2n),(0,1)]` (B) `[(2,n),(0,1)]` (C) `[(1,2n),(0,-1)]` (D) `[(1,n),(0,1)]`

If A=[(1,a),(0, 1)] , then A^n (where n in N) equals (a) [(1,n a),(0, 1)] (b) [(1,n^2a),(0, 1)] (c) [(1,n a),(0 ,0)] (d) [(n,n a),(0,n)]

If A=[{:(,1,a),(,0,1):}] then find lim_(n-oo) (1)/(n)A^(n)

IF A = [(1,0),(1,1)] then for all natural numbers n A^n is equal to (A) [(1,0),(1,n)] (B) [(n,0),(1,1)] (C) [(1,0),(n,1)] (D) none of these

if the product of n matrices [(1,1),(0,1)][(1,2),(0,1)][(1,3),(0,1)]…[(1,n),(0,1)] is equal to the matrix [(1,378),(0,1)] the value of n is equal to

If [{:(1, 1), (0,1):}]*[{:(1, 2), (0,1):}]*[{:(1, 3), (0,1):}]cdotcdotcdot[{:(1, n-1), (0,1):}] = [{:(1, 78), (0,1):}] , then the inverse of [{:(1, n), (0,1):}] is

If A= [(1,0),(1,1)] then (A) A^-n=[(1,0),(-n,1)] , n epsilon N (B) lim_(n rarr 00)1/n^2 A^-n = [(0,0),(0,0)] (C) lim_(nrarroo)1/n A^-n = [(0,0),(-1,0)] (D) none of these

If A=[(2,-1),( 3,-2)] , then A^n= [(1, 0),( 0,1)] , if (a) n is an even natural number (b) [(1 ,0),( 0, 1)] , if n is an odd natural number (c) [(1 ,0),( 0, 1)] , if n in N (d) none of these

If A=[(1,1),(1,0)] and n epsilon N then A^n is equal to (A) 2^(n-1)A (B) 2^nA (C) nA (D) none of these

If A=[(a, b),(0, 1)] , prove that A^n=[(a^n,b((a^n-1)/(a-1))),(0 ,1)] for every positive integer n .

If ((2n+1),(0))+ ((2n+1),(3)) +((2n+1),(6))+ ...= 170, then n equals